One of the problems faced by graduate-level quantum mechanics courses in chemistry is that there is often little time for studying chemical problems. Students must learn so much matrix algebra and notation that a first-semester course seems more like a math or physics course than chemistry. Another problem is the focus of most graduate texts. Excellent texts, such as those by Sakurai, and older treatments, such as Messiah and Cohen-Tannoudji, offer a comprehensive amount of mathematical rigor to go along with chemistry problems, but it seems the intended audience is hard-core theoretical or physical chemistry students. Requirements that are more general, such as reaction-path dynamics, structure and term symbols, and symmetry in quantum mechanical problems, are often left behind. Schatz and Ratner's Book Quantum Mechanics in Chemistry (Prentice Hall) is one book that fills this gap (at least for second-semester students); Simons and Nichols' new book is another, but it is a book that requires revision before it can be seriously considered.

This book's aim is admirable: create a nontraditional approach that jumps right in to chemical problems, with a "pay-as-you-go" approach to the formalism. The first chapter dispenses with history such as the two-slit experiment and Stern-Gerlach. Rather, the student is exposed immediately to operators and wave functions, as well as the Schrödinger equation. Topics in the first section (of six) in the book include one-electron hydrogenic orbitals, Born-Oppenheimer, vibrational-rotational states, and wave functions of nonlinear polyatomics. Section 2 contains simple MO theory. A one- or first-semester course would cover the first two sections, and with these, a student would learn how quantum mechanics applies to some well-known chemistry problems. The complete text contains a full complement of material including molecular spectroscopy and chemical dynamics, and electronic structure calculations.

The formalism is not ignored; there is an appendix that leads the student through the formalism step by step. This is an excellent rudimentary review of the subject, with many worked examples. Additional appendices include Operators and Commutation, Time-Independent Perturbation Theory, Point Group Symmetry, and one on semiempirical methods. Some of this material would be better placed in the main text, as the reader will need to know it anyway. This is especially true for the group theory material. The organization makes for some short chapters: Chapter 2, which covers perturbation theory and the variational method, is only five pages long! All the detail is in the appendices.

One appendix explains the use of electronic structure programs that can be accessed through the World Wide Web. These programs enable MP2, CI, and Hartree-Fock calculations and are adaptable to a number of conditions and systems, though limited to around eight atoms or less. They are written without major optimizations, which makes them easier to understand. They are a welcome part of the book, as the student can explore the programs alone, or the instructor can incorporate them into the class.

The book offers many problems, contained at the end of each section. These range from review exercises to exercises and full-fledged problems, which often are long treatments of a chemical nature, such as the vibration of an N₂ molecule or an SCF treatment of the HeH⁺ molecular system. Full solutions to every type of problem are included. Personally, I would have liked to see the answers to the problems in a separate volume, but having them in the book should at least encourage understanding of the work. The problems themselves are excellent.

So what is the problem? I really wanted to like this book. I feel that the approach is sound, and the wealth of quantum mechanics in chemistry has not been presented in quite this way before. But the text is very difficult to read. The notation is confusing, often nonstandard, and the math is horribly displayed. There are no equation numbers (and therefore no cross-referencing of equations), and it can take a relatively long time to understand what an equation says, even if you are familiar with the topic. Tables and figures are not labeled or numbered. (Not every figure requires a separate caption, but the important ones do.) I find the choices for both displayed math and notation mystifying. Compact notation for partial derivatives is used for some reason, when upright displayed notation would be much better. Such simple mathematical statements as rcos ("rcos(q)") are incomprehensibly crammed together. Referring to molecular orbitals as "mos" instead of "MO's" was also distracting; I think everyone is used to seeing the capitalization. And these are impressions made within the first few chapters! With all the books out there that have little content but are beautifully typeset, I found myself disappointed by the presentation in this book. The typesetting is generally not up to the standards of current publishing. How the manuscript made it past the editors is a mystery to me.

This book could have been an excellent first-semester book for graduate students. It is a chore to read and work with, however. Until it gets at least an editing revision, I would stick with what is currently available.